Paraelectric structure

The diffraction pattern, at room temperature, shows a superposition of a broad peak associated to the ferroelectric phase centered at 20 = 18.97° and a shoulder at 20 = 18.36° corresponding to the non-ferroelectric phase. As the temperature is increased, the intensity of the fainter peak increases and that of the ferroelectric maximum decreases concurrently. At the Curie temperature, the peak characteristic for the ferroelectric structure disappears and only the reflection corresponding to the paraelectric structure is present. On further... 

Initially, it appeared that the phase transitions are purely of the order-disorder type [24]. However, it soon became apparent that atomic displacements also contribute to these phase transitions. These displacements are easy to identify, when one compares the molecular arrangements in the ordered -OH 0= bonds in Fig. 1, with the arrangement of these molecules linked by the disordered bond in Fig. 2. The hydrogen-bonded molecules/ions must rotate before the two H-sites become symmetry-equivalent in the paraelectric phase above Tc- These rotations, usually of few degrees, can be termed as angular displacements. In other words, these angular displacements measure the distortions of the ferroelectric structure where the H-atom ordered from the paraelectric structure where the H-atom is dynamically disordered in two equivalent sites. 

In some materials the antiferroelectric state is barely stable or metastable. In such materials, application of an electric field will convert the phase to ferroelectric, as described, but removal of the field leaves the phase in a ferroelectric state. This material then behaves like a typical ferroelectric and displays a conventional hysteresis loop. Heating the material to a high temperature so as to form the paraelectric structure, followed by cooling, can reform the original antiferroelectric state. 

The phase transiton from a paraelectric to a ferroelectric state, most characteristic for the SbSI type compounds, has been extensively studied for SbSI, because of its importance with respect to the physical properties of this compound (e.g., J53, 173-177, 184, 257). The first-order transition is accompanied by a small shift of the atomic parameters and loss of the center of symmetry, and is most probably of a displacement nature. The true structure of Sb4S5Cl2 106), Bi4S5Cl2 194), and SbTel 108,403) is still unknown. In contrast to the sulfides and selenides of bismuth, BiTeBr 108) and BiTel (JOS, 390) exhibit a layer structure similar to that of the Cdl2 structure, if the difference between Te, Br, and I (see Fig. 36) is ignored. 

Figure 2 shows the schematic structure in the paraelectric (T > Tn) and an-tiferroelectric (T < Tn) phases, hi the paraelectric phase the time-averaged position of the H atoms hes in the middle of an O - H...0 bond, whereas in the antiferroelectric phase, the protons locahze close to one or the other O atom. Prior to the recent NMR work [20-25], the largely accepted model of the phase transition was that the phase transition involved only the ordering of the H atoms in the O - H...0 bonds, and no changes in the electronic structure of the C4 moieties were considered to take place. The NMR results show that, in addition to the order/disorder motion of the H atoms, the transition also involves a change in the electronic charge distribution and symmetry of the C4 squares. 

Whereas the first microscopic theory of BaTiOs [1,2] was based on order-disorder behavior, later on BaTiOs was considered as a classical example of displacive soft-mode transitions [3,4] which can be described by anharmonic lattice dynamics [5] (Fig. 1). BaTiOs shows three transitions at around 408 K it undergoes a paraelectric to ferroelectric transition from the cubic Pm3m to the tetragonal P4mm structure at 278 K it becomes orthorhombic, C2mm and at 183 K a transition into the rhombohedral low-temperature Rm3 phase occurs. 

The structural phase transition for a quantum paraelectric was handled by the following model Hamiltonian [2] ... 

Ferroelectric-paraelectric transitions can be understood on the basis of the Landau-Devonshire theory using polarization as an order parameter (Rao Rao, 1978). Xhe ordered ferroelectric phase has a lower symmetry, belonging to one of the subgroups of the high-symmetry disordered paraelectric phase. Xhe exact structure to which the paraelectric phase transforms is, however, determined by energy considerations. 

Fig. 16a-c. Schematic model of the lamellar structure of the copolymer in the, a. high temperature range (paraelectric phase) b. Curie transition region and c. low temperature region L and I denote respectively the long period and the average crystal thickness comprising a mixture of non ferroelectric and ferroelectric domains... 

In the article by Balta Calleja et al., the latest results of investigations into the structure of poly(vinylidenefluoride)and its copolymers withpoly(trifluoroethylene) are summarized and extensively dicussed. These polymers are the most important ferroelectric materials. Special emphasis is placed on the relation between the change of structure and the transition from the ferroelectric into the paraelectric phase. 

All of structures (3) relate to antiferroelectric phase that is in an agreement with the available measurements evidencing just the same character of low-temperature phase in the M3D(A04)2 crystals [6], It is also evident that the doubling of b-parameter of the paraelectric A2/a cell under transition to the low-temperature D-ordered phase directly follows from proposed scheme (3). Recently, such fe-doubling is observed experimentally in [7]. This scheme is also consistent with the doubling of c-parameter of A2/a cell found in the cited paper. In particular, such fe-doubling takes place when the layer sequence (3) takes the form ... 

All cations are located within the equatorial plane of the 02--octahedra in the paraelectric high-temperature phase [15], In this case the crystal belongs to the centrosymmetric space group P4/mbm. In the low-temperature phase the metal atoms are displaced out of this plane. As a result the crystal structure is transferred into the polar space group P4bm and the polar... 

In the paraelectric phase at T > Tm, where polar clusters vanish and beam-coupling is not possible because the polar macrostructure is no longer present, only the weak seed scattering is observed. Due to the drastic changes in the domain structure at the phase transition, the seed scattering at 130 °C differs from that at 28 °C both in the total amount and in the angular distribution. 

In conclusion, detailed information on changes in the polar structure of sisniCc after application of external electric fields as well as during the ferroelectric-paraelectric phase transition is received from the study of the initially scattered light. Strong hints are revealed that the relaxor-kind phase transition in sbn is due to a dispersion of the thermal decay for different spatial scales in the polar structure. 

The perovskite structure is, of course, of special significance in the electroceramics context since the ferroelectric perovskites are dominant in the ceramic capacitor, PTC thermistor and electromechanical transducer industries. The structure favours the existence of soft modes (low frequency phonons) as evidenced by its tendency to instability, for example the ferroelectric-paraelectric transition. Instability is evident in the case of the T23 compound which exhibits a tetragonal-orthorhombic transition in the region of 700 °C (the exact temperature depends on the oxygen content). Extensive twinning, very reminiscent of ferroelectric domain structures, is observed. 

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